Dataset Information

Empirical Bayes inference of pairwise F(ST) and its distribution in the genome.

ABSTRACT: Populations often have very complex hierarchical structure. Therefore, it is crucial in genetic monitoring and conservation biology to have a reliable estimate of the pattern of population subdivision. F(ST)'s for pairs of sampled localities or subpopulations are crucial statistics for the exploratory analysis of population structures, such as cluster analysis and multidimensional scaling. However, the estimation of F(ST) is not precise enough to reliably estimate the population structure and the extent of heterogeneity. This article proposes an empirical Bayes procedure to estimate locus-specific pairwise F(ST)'s. The posterior mean of the pairwise F(ST) can be interpreted as a shrinkage estimator, which reduces the variance of conventional estimators largely at the expense of a small bias. The global F(ST) of a population generally varies among loci in the genome. Our maximum-likelihood estimates of global F(ST)'s can be used as sufficient statistics to estimate the distribution of F(ST) in the genome. We demonstrate the efficacy and robustness of our model by simulation and by an analysis of the microsatellite allele frequencies of the Pacific herring. The heterogeneity of the global F(ST) in the genome is discussed on the basis of the estimated distribution of the global F(ST) for the herring and examples of human single nucleotide polymorphisms (SNPs).

SUBMITTER: Kitada S

PROVIDER: S-EPMC2034649 | biostudies-other | 2007 Oct

REPOSITORIES: biostudies-other

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Empirical Bayes inference of pairwise F(ST) and its distribution in the genome.

Kitada Shuichi S Kitakado Toshihide T Kishino Hirohisa H

Genetics 20070729 2

Populations often have very complex hierarchical structure. Therefore, it is crucial in genetic monitoring and conservation biology to have a reliable estimate of the pattern of population subdivision. F(ST)'s for pairs of sampled localities or subpopulations are crucial statistics for the exploratory analysis of population structures, such as cluster analysis and multidimensional scaling. However, the estimation of F(ST) is not precise enough to reliably estimate the population structure and th ...[more]

PMID: 17660541

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Project description:BackgroundMicroarray data enables the high-throughput survey of mRNA expression profiles at the genomic level; however, he data presents a challenging statistical problem because of the large number of transcripts with small sample sizes that are obtained. To reduce the dimensionality, various Bayesian or empirical Bayes hierarchical models have been developed. However, because of the complexity of the microarray data, no model can explain the data fully. It is generally difficult to scrutinize the irregular patterns of expression that are not expected by the usual statistical gene by gene models.ResultsAs an extension of empirical Bayes (EB) procedures, we have developed the ?-empirical Bayes (?-EB) approach based on a ?-likelihood measure which can be regarded as an 'evidence-based' weighted (quasi-) likelihood inference. The weight of a transcript t is described as a power function of its likelihood, f?(yt|?). Genes with low likelihoods have unexpected expression patterns and low weights. By assigning low weights to outliers, the inference becomes robust. The value of ?, which controls the balance between the robustness and efficiency, is selected by maximizing the predictive ??-likelihood by cross-validation. The proposed ?-EB approach identified six significant (p<10??) contaminated transcripts as differentially expressed (DE) in normal/tumor tissues from the head and neck of cancer patients. These six genes were all confirmed to be related to cancer; they were not identified as DE genes by the classical EB approach. When applied to the eQTL analysis of Arabidopsis thaliana, the proposed ?-EB approach identified some potential master regulators that were missed by the EB approach.ConclusionsThe simulation data and real gene expression data showed that the proposed ?-EB method was robust against outliers. The distribution of the weights was used to scrutinize the irregular patterns of expression and diagnose the model statistically. When ?-weights outside the range of the predicted distribution were observed, a detailed inspection of the data was carried out. The ?-weights described here can be applied to other likelihood-based statistical models for diagnosis, and may serve as a useful tool for transcriptome and proteome studies.

Project description:Characterizing the distribution of effects from genome-wide genotyping data is crucial for understanding important aspects of the genetic architecture of complex traits, such as number or proportion of non-null loci, average proportion of phenotypic variance explained per non-null effect, power for discovery, and polygenic risk prediction. To this end, previous work has used effect-size models based on various distributions, including the normal and normal mixture distributions, among others. In this paper we propose a scale mixture of two normals model for effect size distributions of genome-wide association study (GWAS) test statistics. Test statistics corresponding to null associations are modeled as random draws from a normal distribution with zero mean; test statistics corresponding to non-null associations are also modeled as normal with zero mean, but with larger variance. The model is fit via minimizing discrepancies between the parametric mixture model and resampling-based nonparametric estimates of replication effect sizes and variances. We describe in detail the implications of this model for estimation of the non-null proportion, the probability of replication in de novo samples, the local false discovery rate, and power for discovery of a specified proportion of phenotypic variance explained from additive effects of loci surpassing a given significance threshold. We also examine the crucial issue of the impact of linkage disequilibrium (LD) on effect sizes and parameter estimates, both analytically and in simulations. We apply this approach to meta-analysis test statistics from two large GWAS, one for Crohn's disease (CD) and the other for schizophrenia (SZ). A scale mixture of two normals distribution provides an excellent fit to the SZ nonparametric replication effect size estimates. While capturing the general behavior of the data, this mixture model underestimates the tails of the CD effect size distribution. We discuss the implications of pervasive small but replicating effects in CD and SZ on genomic control and power. Finally, we conclude that, despite having very similar estimates of variance explained by genotyped SNPs, CD and SZ have a broadly dissimilar genetic architecture, due to differing mean effect size and proportion of non-null loci.

Dataset Information

Empirical Bayes inference of pairwise F(ST) and its distribution in the genome.

Publications

Empirical Bayes inference of pairwise F(ST) and its distribution in the genome.

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